Difference between revisions of "Luck"

m (→‎The Math: Unnecessary pluralization.)
m (→‎The Math: Simplified with Bomb Bloke's mysterious natural logarithmic identity shortcut.)
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If one wishes to derive the chance to raise loot level, C, that they have based on their current level of Luck, L, the equation can be solved for C as follows:
 
If one wishes to derive the chance to raise loot level, C, that they have based on their current level of Luck, L, the equation can be solved for C as follows:
−
* L = C^1.8
+
# L = C^1.8
−
* ln(L) = 1.8 * ln(C)
+
# ln(L) = 1.8 * ln(C)
−
* ln(L) / 1.8 = ln(C)
+
# ln(L) / 1.8 = ln(C)
−
* e^(ln(L) / 1.8) = e^ln(C)
+
# e^(ln(L) / 1.8) = e^ln(C)
−
* '''e^(ln(L) / 1.8) = C'''
+
# '''e^(ln(L) / 1.8) = C'''
−
** Where e = 2.71828 18284 59045 23536...
+
#* Where e = 2.71828 18284 59045 23536...
  
 
With access to a scientific calculator, this can easily be solved.
 
With access to a scientific calculator, this can easily be solved.
 
* Example: Your suit gives you 1500 Luck. Your chance to get more and greater loot is e^(ln(1500) / 1.8) = 58.1426931, or approximately 58%.
 
* Example: Your suit gives you 1500 Luck. Your chance to get more and greater loot is e^(ln(1500) / 1.8) = 58.1426931, or approximately 58%.
  
−
If you don't have a scientific calculator, then the equation can be simplified back to its original form and solved for C as follows:
+
If you don't have a scientific calculator, then the equation can be further simplified and solved for C as follows:
−
* e^(ln(L) / 1.8) = C
+
# e^(ln(L) / 1.8) = C
−
* (e^(ln(L) / 1.8))^1.8 = C^1.8
+
# e^(ln(L) / 1.8) = C^ln(e)
−
* e^((ln(L) / 1.8) * 1.8) = C^1.8
+
# L^(ln(e) / 1.8) = C^1
−
* e^((ln(L) * 1.8) / 1.8) = C^1.8
+
# L^(1 / 1.8) = C
−
* e^((ln(L) / 1) * (1.8 / 1.8)) = C^1.8
+
# '''L^(5 / 9) = C'''
−
* e^(ln(L) * 1) = C^1.8
+
−
* e^ln(L) = C^1.8
+
−
* L = C^1.8
+
−
* L^(1 / 1.8) = (C^1.8)^(1 / 1.8)
+
−
* L^(5 / 9) = C^(1.8 * (1 / 1.8))
+
−
* L^(5 / 9) = C^((1.8 / 1) * (1 / 1.8))
+
−
* L^(5 / 9) = C^(1.8 / 1.8)
+
−
* L^(5 / 9) = C^1
+
−
* '''L^(5 / 9) = C'''
+
  
 
This equation is then quite easy to solve.
 
This equation is then quite easy to solve.

Revision as of 23:45, 14 March 2009

Luck is an item property found on various equippable items. Luck stacks across all items that a character has equipped to make up their Luck score, which can be viewed on the Character Status Menu. This Luck score can then be augmented by various temporary Luck boosts from other sources.

A character's total Luck is used when loot is spawned on creature corpses. It gives a chance of there being a greater amount of loot, a chance of a greater number of properties on said loot, and a chance that those properties will be of greater intensity. It should be noted, however, that this is only a chance of more and greater loot, and that Luck has no direct affect on what specific items will spawn and what specific properties will spawn on those items.

Equippables

Armor, shields, or weapons can be made from or enhanced by golden ingots, spined leather, yellow dragon scales, or oak boards, depending on the type of item, in order to gain or increase the Luck property. Using golden ingots, spined leather, or oak boards will either give an item the Luck property with a default value of 40, or, if the item already possesses the Luck property, will increase it by 40. Yellow dragon scales can be used to craft pieces of Dragon Armor, each with a default amount of 20 Luck. Newly created armor of any type that is crafted with Runic Tools has a chance to be created with the Luck property with a value up to 100, which stacks with any material-related Luck bonuses.

The types of items that can be crafted or enhanced with the Luck property are listed below, categorized by material type:

Armor, shields, and weapons can spawn on monster corpses with the Luck property, with values up to and including 100. These items can then be enhanced with golden ingots, spined leather, or oak boards, depending on their material type, thus allowing them to have up to 140 Luck.

Other Sources

The 10th Anniversary Sculpture, when double-clicked while in a character's backpack or locked down in a house, grants a character a base bonus of 200 Luck plus 50 Luck for each year in the age of the account that the character is on.

A minor bonus can be obtained from the Sphynx located in the Forgotten Pyramid. A player can pay the Sphynx 5000 gold to "tell them their fortune." If, after giving the Sphynx the 5000 gold, it responds "Fate smiles upon you this day." your character will receive a 24-hour boost of from 1 to 80 Luck.

The Bushido ability Perfection also results in a Luck bonus. A character with at least 50 Bushido skill can Honor a creature and then attempt to hit that creature as many times as they can. The character receives a score based on the number of consecutive hits achieved and is then rewarded a Luck bonus equal to ten percent of the square of this score. The maximum score is 100, thus the maximum Luck bonus from Perfection is 100^2 x 0.1 = 1000.

Artifacts

Some artifacts and other items spawn, have spawned, or can be crafted, with a default amount of Luck on them.

Event Items

In the past, several items stemming from the Event Moderator system have possessed the Luck property.

  • Exceptional Robe Crafted by Relvinian (Lost) - Luck 250
  • Orc Chieftain Helm (Original and Replica) - Luck 100
  • The Protector - Luck 100
  • Royal Guard Boots - Luck 50
  • Royal Guard Survival Knife - Luck 100
    • Enhanced Version - Luck 140
  • The Wild's Call - Luck 100

Affect on Normal Loot

The Roll

Normal loot that spawns on creature corpses, other than gold and a few other special items, is generated upon the death of the creature, not before. Upon the death of the creature, a roll is made against the Luck of the character who did the most damage, I.e. "the top attacker," on a scale of 0-99 in order to determine whether there is a loot increase. The process can be explained in the following steps:

  1. The RNG generates a number from 0-99.
  2. The top attacker's Luck is evaluated to determine their percentage (%) chance value, which is derived from the equation
    • Chance = Luck^(5 / 9)
      • (This equation is explained fully in the Math section below.)
  3. This percentage (%) chance value is then rounded to a whole number.
  4. The rounded percentage (%) chance value is then compared against the number generated by the RNG as follows:
    • If (Luck percentage (%) chance value > RNG value)
          Increase loot
      Else
          Do not increase loot
  • Example: The RNG rolls a 30. The top attacker's Luck is evaluated and results in a rounded percentage (%) chance value of 56. 56 > 30, so the loot is increased.

This roll applies to all loot that is spawned, even that which is given to other attackers in their own instanced corpses; the top attacker's Luck applies to everyone.

Number of Items

Each type of creature in the game has its loot determined by predefined loot tables that dictate both the type of loot available and the number of items that can spawn. The number of items that spawn on a particular creature's corpse is a random number in the range of one (1) to a maximum number as defined in that creature's loot table. When a creature is killed, if the roll made against the top attacker's Luck score is successful, the number of items spawned on the creature's corpse will be increased by one (1), unless this new amount would be greater than that creature's loot amount cap.

  • Example: A particular creature's loot amount cap is 10 items. A character with high Luck kills the creature, the game rolls against the character's Luck score, and the roll is in favor of the character. The game rolls and decides to spawn 10 items on the corpse, which is increased by 1 from the top attacker's Luck roll, resulting in 11 items being spawned. However, this is greater than the creature's loot amount cap of 10 items, so only 10 items spawn, instead of 11.

Number of Item Properties

In the same way that creature loot tables define the number of items that drop on a particular creature's corpse, they also define the number of properties that can spawn on those items. The number of properties that spawn on an item that is dropped by a particular creature is a random number in the range of one (1) to a maximum number as defined in that creature's loot table. When an item is spawned on a creature's corpse, if the roll made against the top attacker's Luck score is successful, the number of properties spawned on the item will be increased by one (1), unless this new amount would be greater than that creature's loot amount cap.

  • Example: A particular creature's cap on the number of properties per item is 3 properties. A character with high Luck kills the creature, the game rolls against the character's Luck score, and the roll is in favor of the character. The game rolls and decides to put 3 properties on the first item spawned on the corpse, which is increased by 1 from the top attacker's Luck roll, resulting in 4 properties being spawned on the item. However, this is greater than the creature's cap of 3 on the number of properties per item, so only 3 properties spawn on the item, instead of 4.

Item Property Intensities

Creature loot tables also define the range of intensity of item properties on items that drop on various creature corpses. The intensity of a property on an item dropped by a particular creature is a random number within a range which is a subset of the entire range of a particular property. When a property is spawned on an item on a creature's corpse, if the roll made against the top attacker's Luck score is successful, the property's intensity will be increased by 10% of the property's overall maximum value, unless this new amount would be greater than the top end of the possible intensity range of that creature.

  • Example: The overall range for a particular property is 1 to 50. A particular creature's item property intensity range is 0.25 to 0.3, which results in possible values of that property of 13, 14, or 15. A character with high Luck kills the creature, the game rolls against the character's Luck score, and the roll is in favor of the character. The game spawns a weapon on the creature's corpse with that property with an initial value of 14, which is increased by 10% of the overall maximum value of 50 (5), resulting in a property value of 19. However, this is greater than the creature's cap of 15, so the property is capped at 15, instead of 19.

Affect on the Gauntlet

(Editor: This section is not really accurate anymore. The Gauntlet now uses the Treasures of Tokuno points system, so the following info is probably only a shadow of the truth, if that. This will be changed in the future when further information becomes available.)

When a boss dies in the Doom Gauntlet there is a certain chance that an artifact will be created. This chance is influenced by the Luck of the top attacker, and can be derived from the following equation:

  • C - ((sqr(L) * C) / 100) = NC
    • C = Chance (1 in C) for an Artifact to be Created
    • L = Luck of the Top Attacker
    • NC = New Chance for an Artifact to be Created

Example: Suppose there is a 1 in 20 (5%) chance that an artifact will be generated when the Dark Father is killed, and the Luck of the top attacker is 900.

  • 20 - ((sqr(900) * 20) / 100) = NC
  • 20 - ((30 * 20) / 100) = NC
  • 20 - (600 / 100) = NC
  • 20 - 6 = NC
  • 14 = NC

The new chance for an artifact to be generated is 1 in 14 (~7.1%). If, based on this new percentage chance, an artifact is actually generated, it is then distributed randomly amongst all players that receive looting rights.

Affect on Other Loot

Power Scrolls that drop from Champion Spawns are not affected whatsoever by the Luck of any attacker, and are generated and distributed randomly amongst all players that receive looting rights.

The Math

Luck is evaluated in the context of a logarithmic equation, which is frequently referred to colloquially as "diminishing returns." It is true that your Luck chance will increase the more Luck you have, but it is not a linear increase. The more Luck you have, the more you need to add to it to experience increases in your Luck chance.

  • Example: To have a 10% Luck chance, you need approximately 63.1 Luck. One would assume that to have a 20% Luck chance, you would need 63.1 x 2 = 126.2 Luck, but this is not the case. To have a 20% Luck chance you would actually need approximately 219.7 Luck.

Luck's logarithmic equation is as follows:

  • L = C^1.8
    • L = Luck Required
    • C = Chance to Raise Loot Level.

One can substitute the percentage chance that they wish to achieve for the variable C, and thus derive the amount of Luck required to achieve it, L.

  • Example: You wish to obtain a 50% chance of more and greater loot. The Luck required to do this is 50^1.8 = 1143.2626298183158660067558096781, or, rounding up because Luck only exists in integer amounts, 1144.

If one wishes to derive the chance to raise loot level, C, that they have based on their current level of Luck, L, the equation can be solved for C as follows:

  1. L = C^1.8
  2. ln(L) = 1.8 * ln(C)
  3. ln(L) / 1.8 = ln(C)
  4. e^(ln(L) / 1.8) = e^ln(C)
  5. e^(ln(L) / 1.8) = C
    • Where e = 2.71828 18284 59045 23536...

With access to a scientific calculator, this can easily be solved.

  • Example: Your suit gives you 1500 Luck. Your chance to get more and greater loot is e^(ln(1500) / 1.8) = 58.1426931, or approximately 58%.

If you don't have a scientific calculator, then the equation can be further simplified and solved for C as follows:

  1. e^(ln(L) / 1.8) = C
  2. e^(ln(L) / 1.8) = C^ln(e)
  3. L^(ln(e) / 1.8) = C^1
  4. L^(1 / 1.8) = C
  5. L^(5 / 9) = C

This equation is then quite easy to solve.

  • Example: Your suit gives you 1500 Luck. Your chance to get more and greater loot is 1500^(5 / 9) = 58.1426931, or approximately 58%, which is the same answer as that derived from the former equation involving e.

Maximum Luck

There is frequently much debate and mathematical figuring going on within the community about what the maximum attainable Luck is for a single character. This debate is usually reignited every time a new item is introduced into the game that has a high amount of Luck on it, and results in several different answers, depending on whether or not you include event items, Luck granted by the 10th Anniversary Sculpture, samurai Perfection, etcetera.

Just counting items that currently spawn in-game or are relatively (or in the case of the Adventurer's Machete / Luckblade, theoretically) easy to obtain, the current maximum Luck that a single character can achieve is as follows:

If you replace the Robe of the Eclipse with now the lost Exceptional Robe Crafted by Relvinian, and also equip a pair of Royal Guard Boots, the total becomes:

  • Total: 150 + 200 + 200 + 140 + 140 + 140 + 160 + 80 + 400 + 250 + 50 = 1910 Luck

If you then add in the Luck bonus from the 10th Anniversary Sculpture, which is a base 200 Luck plus 50 Luck for each year of account age, thus resulting in a maximum attainable amount of 750 Luck (on an 11-year-old account), the total becomes:

  • Total: 150 + 200 + 200 + 140 + 140 + 140 + 160 + 80 + 400 + 250 + 50 + 750 = 2660 Luck

If you then add in the maximum Luck bonus obtainable from the Sphynx, the total becomes:

  • Total: 150 + 200 + 200 + 140 + 140 + 140 + 160 + 80 + 400 + 250 + 50 + 750 + 80 = 2740 Luck

Finally, if you possess the Bushido skill, Honor your intended target, and then achieve Perfection, you will be granted a 1000 Luck bonus. Adding this to what we already have, the total becomes:

  • Total: 150 + 200 + 200 + 140 + 140 + 140 + 160 + 80 + 400 + 250 + 50 + 750 + 80 + 1000 = 3740 Luck

If you take away the Exceptional Robe Crafted by Relvinian, which can no longer be obtained by anyone as it no longer exists in the game, and reintroduce the Robe of the Eclipse in its stead, you come out with:

  • Total: 150 + 200 + 200 + 140 + 140 + 140 + 160 + 80 + 400 + 95 + 50 + 750 + 80 + 1000 = 3585 Luck

Logically, however, no matter how high the Maximum Luck number grows over time as new and better items and abilities are introduced into the game, the highest Luck that will ever be useful will be the amount of Luck required to have a 100% chance of more and greater loot. By the Luck equation in the last section, we can easily determine this number:

  • L = 100^1.8 = 3981.0717055349725077025230508775, or, rounding up because Luck exists only in integer amounts, 3982 Luck.

See Also


Template:Item properties

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